Preflop: Against that kind of opponent fold all day long. I'd never 3bet against that kind of guy unless I know that he is capable of folding to 3bets or either folding postflop. But it's not the case, therefore fold.

As playedFlop: I'd raise it ~$2,50.Turn: Kinda close, I guess I'd raise a bit bigger ~$4 or sometimes I even just Call, since he will anyways, have hard time Calling with a lot worse. Unless he is loose enough.River: And here I'd just ship it, since it's very unlikely him to have the Q that often here anyways, more often has some kind of other hand, maybe an overpair or even Tx which is going to Call.